Question

the pythagorean theorem
write an equation you could use to find the length of the missing side
of each right triangle. then find the missing length. round to the
nearest tenth if necessary.
1.
2.
3.

4.
5.
6.

1. (a), 65 cm; (c), 95 cm
2. (a), 16 yd; (b), 22 yd

determine whether each triangle with sides of given lengths is a
right triangle. justify your answer.

1. 18 ft, 23 ft, 29 ft
2. 7 yd, 24 yd, 25 yd

1. the hypotenuse of a right triangle is 15 inches, and one of its legs is

11 inches. find the length of the other leg.

1. a leg of a right triangle is 30 meters long, and the hypotenuse is

35 meters long. what is the length of the other leg?

1. televisions the diagonal of a television measures 27 inches. if the width

of a 27 - inch is 22 inches, calculate its height to the nearest inch.

Explanation:

Problem 1

Step1: Apply Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\), here \(a = 8\), \(c = 10\), so \(8^{2}+b^{2}=10^{2}\)

Step2: Solve for \(b\)

\(64 + b^{2}=100\), \(b^{2}=100 - 64 = 36\), \(b=\sqrt{36}=6\)

Step1: Apply Pythagorean theorem

\(24^{2}+a^{2}=26^{2}\)

Step2: Solve for \(a\)

\(576+a^{2}=676\), \(a^{2}=676 - 576 = 100\), \(a=\sqrt{100}=10\)

Step1: Apply Pythagorean theorem

\(18^{2}+15^{2}=c^{2}\)

Step2: Solve for \(c\)

\(324 + 225=c^{2}\), \(c^{2}=549\), \(c=\sqrt{549}\approx23.4\)

Answer:

\(b = 6\) ft

Problem 2